After going through some cutscenes and a brief exploration bit in your therapist's office, you'll be transported to a hospital. You automatically enter the room where your mother was staying. Once you gain control of Alex, walk over to the first countertop on your right. The purse resting on the counter has "Mom's Keys" that you'll need to interact with. Hold "LT" and then the "A" button, listen to the memory play out and the achievement will pop!